Question

A tree has a 25% chance of flowering. In a random sample of 15 trees, what is the probability that at least 4 develop flowers?

Answer 1

To find the probability that at least 4 out of 15 trees develop flowers, we use the binomial probability formula. We calculate the probability for each possible number of trees developing flowers and sum them up.

Step-by-step explanation:

To find the probability that at least 4 out of 15 trees develop flowers, we will use the binomial probability formula.

First, we need to calculate the probability that exactly 3 trees develop flowers. Using the binomial probability formula, this can be calculated as:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

P(X = 3) = C(15, 3) * 0.25^3 * 0.75^(15-3)

Next, we calculate the probability that exactly 2 trees develop flowers. P(X = 2) = C(15, 2) * 0.25^2 * 0.75^(15-2)

We continue this process until we calculate the probability for exactly 3 trees, 2 trees, 1 tree, and 0 trees developing flowers. Then, we sum up these probabilities to find the probability that at least 4 trees develop flowers.

Answer 2

15 * .25 = 3.75 so slim to none